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Dehghan, Mehdi, Karamali, Gholamreza, Shirilord, Akbar. (1403). An iterative scheme for a class of generalized Sylvester matrix equations. نشریه مهندسی عمران امیرکبیر, 5(3), 195-215. doi: 10.22060/ajmc.2024.22444.1159
Mehdi Dehghan; Gholamreza Karamali; Akbar Shirilord. "An iterative scheme for a class of generalized Sylvester matrix equations". نشریه مهندسی عمران امیرکبیر, 5, 3, 1403, 195-215. doi: 10.22060/ajmc.2024.22444.1159
Dehghan, Mehdi, Karamali, Gholamreza, Shirilord, Akbar. (1403). 'An iterative scheme for a class of generalized Sylvester matrix equations', نشریه مهندسی عمران امیرکبیر, 5(3), pp. 195-215. doi: 10.22060/ajmc.2024.22444.1159
Dehghan, Mehdi, Karamali, Gholamreza, Shirilord, Akbar. An iterative scheme for a class of generalized Sylvester matrix equations. نشریه مهندسی عمران امیرکبیر, 1403; 5(3): 195-215. doi: 10.22060/ajmc.2024.22444.1159

An iterative scheme for a class of generalized Sylvester matrix equations

AUT Journal of Mathematics and Computing
دوره 5، شماره 3، 2024، صفحه 195-215    اصل مقاله (1.94 M)
نوع مقاله: Original Article
شناسه دیجیتال (DOI): 10.22060/ajmc.2024.22444.1159
نویسندگان
Mehdi Dehghan* 1؛ Gholamreza Karamali2؛ Akbar Shirilord1
1Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran
2Faculty of Basic Sciences, Shahid Sattari Aeronautical University of Sciences and Technology, South Mehrabad, Tehran, Iran
چکیده
In this study based on the accelerated over relaxation (AOR) method we make an iterative scheme for solving generalized Lyapunov matrix equation
$$ {A}{X}+{X}{B}+\sum_{j=1}^{m}{N}_j{X}{M}_j={C},$$
over complex or real matrices. Then we analyze the convergence of the new iterative method in detail. There have been discussions for the calculation of optimal parameters. Finally a numerical example is given to demonstrate the capability of the new method.
کلیدواژه‌ها
Optimal parameters؛ Complex matrices؛ Generalized Sylvester matrix equation؛ Accelerated over relaxation (AOR) method؛ Control theory
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